## TRIANGLE WORKSHEET SOLUTION 4

Triangle Worksheet Solution 4 :

In this section, you will have solutions for the problems on finding area of a triangle when three of its vertices are given.

(4) In each of the following, find the value of k for which the given points are collinear.

(i) (k, -1)  ( 2, 1) and (4, 5)

Solution :

If the given points are collinear then the area of triangle is zero

(1/2) [(k + 10 – 4) – (-2 + 4 + 5k)] = 0

[(k + 6) – (2+ 5k)] = 0 x 2

(k + 6 – 2 - 5k) = 0

-4 k + 4 = 0

- 4k = -4

K = (-4)/(-4)

K = 1

Hence, the value of k is 1

(ii) (2, -5)  ( 3, -4) and (9, k)

Solution :

If the given points are collinear then the area of triangle is zero

(1/2) [(-8 + 3k – 45) – (-15 - 36 + 2k)]  =  0

[(3k - 53) – (-51+ 2k)]  =  0 x 2

(3k - 53 + 51- 2k)  =  0

k - 2  =  0

k  =  2

Hence the value of k is 2

(iii) (k, k)  (2, 3) and (4, -1)

Solution :

If the given points are collinear then the area of triangle is zero

(1/2) [(3k - 2 + 4k) – (2k + 12 - k)]  =  0

[(7k - 2) – (k+12)]  =  0 x 2

(7k - 2 – k - 12)  =  0

6 k - 14  =  0

6k  =  14

K  =  14/6

K  = 7/3

Hence the value of k is 7/3

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